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A hybrid model of mammalian cell cycle regulation.

Singhania R, Sramkoski RM, Jacobberger JW, Tyson JJ - PLoS Comput. Biol. (2011)

Bottom Line: Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation.The few kinetic constants in the model are easily estimated from the experimental data.Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States of America.

ABSTRACT
The timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. It is difficult to estimate these kinetic constants from available experimental data. To avoid this problem, modelers often resort to 'qualitative' modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this paper we describe a hybrid approach that combines the best features of continuous differential equations and discrete Boolean networks. Cyclin abundances are tracked by piecewise linear differential equations for cyclin synthesis and degradation. Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation. The discrete variables change according to a predetermined sequence, with the times between transitions determined in part by cyclin accumulation and degradation and as well by exponentially distributed random variables. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. The few kinetic constants in the model are easily estimated from the experimental data. Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.

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Model predictions of cyclin E dynamics.(A) Scatter plots. (B) Stochastic limit cycle in the state space of cyclins A, B and E. We provide two different perspectives of this three dimensional figure to help visualize how the cyclin levels go up and down. In addition, we have added golden-colored balls to help guide the eye along the cell cycle trajectory. Each ball represents the average of the cyclin levels of all the cells binned over a hundredth of the ϕi interval [0,1], where ϕi refers to the fraction of the cell cycle completed by cell i (as described in the Methods section). Finally, it may help to recognize that Fig. 2E is a projection of the data on the CycA-CycB plane, and Fig. 3B is a projection on the CycA-CycE plane.
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pcbi-1001077-g003: Model predictions of cyclin E dynamics.(A) Scatter plots. (B) Stochastic limit cycle in the state space of cyclins A, B and E. We provide two different perspectives of this three dimensional figure to help visualize how the cyclin levels go up and down. In addition, we have added golden-colored balls to help guide the eye along the cell cycle trajectory. Each ball represents the average of the cyclin levels of all the cells binned over a hundredth of the ϕi interval [0,1], where ϕi refers to the fraction of the cell cycle completed by cell i (as described in the Methods section). Finally, it may help to recognize that Fig. 2E is a projection of the data on the CycA-CycB plane, and Fig. 3B is a projection on the CycA-CycE plane.

Mentions: In Fig. 2 we compare our simulated flow-cytometry scatter plots with experimental results of Yan et al. [42]. We color-code each cell in the simulated plot according to which Boolean State (Table 1) the cell is in at the time of fixation. In Fig. 3 we plot cyclin E fluctuations, as predicted by our model, along with a projection of the cell cycle trajectory in a subspace spanned by the three cyclin variables (A, B and E).


A hybrid model of mammalian cell cycle regulation.

Singhania R, Sramkoski RM, Jacobberger JW, Tyson JJ - PLoS Comput. Biol. (2011)

Model predictions of cyclin E dynamics.(A) Scatter plots. (B) Stochastic limit cycle in the state space of cyclins A, B and E. We provide two different perspectives of this three dimensional figure to help visualize how the cyclin levels go up and down. In addition, we have added golden-colored balls to help guide the eye along the cell cycle trajectory. Each ball represents the average of the cyclin levels of all the cells binned over a hundredth of the ϕi interval [0,1], where ϕi refers to the fraction of the cell cycle completed by cell i (as described in the Methods section). Finally, it may help to recognize that Fig. 2E is a projection of the data on the CycA-CycB plane, and Fig. 3B is a projection on the CycA-CycE plane.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3037389&req=5

pcbi-1001077-g003: Model predictions of cyclin E dynamics.(A) Scatter plots. (B) Stochastic limit cycle in the state space of cyclins A, B and E. We provide two different perspectives of this three dimensional figure to help visualize how the cyclin levels go up and down. In addition, we have added golden-colored balls to help guide the eye along the cell cycle trajectory. Each ball represents the average of the cyclin levels of all the cells binned over a hundredth of the ϕi interval [0,1], where ϕi refers to the fraction of the cell cycle completed by cell i (as described in the Methods section). Finally, it may help to recognize that Fig. 2E is a projection of the data on the CycA-CycB plane, and Fig. 3B is a projection on the CycA-CycE plane.
Mentions: In Fig. 2 we compare our simulated flow-cytometry scatter plots with experimental results of Yan et al. [42]. We color-code each cell in the simulated plot according to which Boolean State (Table 1) the cell is in at the time of fixation. In Fig. 3 we plot cyclin E fluctuations, as predicted by our model, along with a projection of the cell cycle trajectory in a subspace spanned by the three cyclin variables (A, B and E).

Bottom Line: Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation.The few kinetic constants in the model are easily estimated from the experimental data.Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States of America.

ABSTRACT
The timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. It is difficult to estimate these kinetic constants from available experimental data. To avoid this problem, modelers often resort to 'qualitative' modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this paper we describe a hybrid approach that combines the best features of continuous differential equations and discrete Boolean networks. Cyclin abundances are tracked by piecewise linear differential equations for cyclin synthesis and degradation. Cyclin synthesis is regulated by transcription factors whose activities are represented by discrete variables (0 or 1) and likewise for the activities of the ubiquitin-ligating enzyme complexes that govern cyclin degradation. The discrete variables change according to a predetermined sequence, with the times between transitions determined in part by cyclin accumulation and degradation and as well by exponentially distributed random variables. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. The few kinetic constants in the model are easily estimated from the experimental data. Using this hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks in cells.

Show MeSH